279 research outputs found
Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics
By resorting to the Fock--Bargmann representation, we incorporate the quantum
Weyl--Heisenberg (-WH) algebra into the theory of entire analytic functions.
The main tool is the realization of the --WH algebra in terms of finite
difference operators. The physical relevance of our study relies on the fact
that coherent states (CS) are indeed formulated in the space of entire analytic
functions where they can be rigorously expressed in terms of theta functions on
the von Neumann lattice. The r\^ole played by the finite difference operators
and the relevance of the lattice structure in the completeness of the CS system
suggest that the --deformation of the WH algebra is an essential tool in the
physics of discretized (periodic) systems. In this latter context we define a
quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz
Spin network setting of topological quantum computation
The spin network simulator model represents a bridge between (generalised)
circuit schemes for standard quantum computation and approaches based on
notions from Topological Quantum Field Theories (TQFTs). The key tool is
provided by the fiber space structure underlying the model which exhibits
combinatorial properties closely related to SU(2) state sum models, widely
employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.Comment: Proc. "Foundations of Quantum Information", Camerino (Italy), 16-19
April 2004, to be published in Int. J. of Quantum Informatio
Isentropic Curves at Magnetic Phase Transitions
Experiments on cold atom systems in which a lattice potential is ramped up on
a confined cloud have raised intriguing questions about how the temperature
varies along isentropic curves, and how these curves intersect features in the
phase diagram. In this paper, we study the isentropic curves of two models of
magnetic phase transitions- the classical Blume-Capel Model (BCM) and the Fermi
Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods
are used. The isentropic curves of the BCM generally run parallel to the phase
boundary in the Ising regime of low vacancy density, but intersect the phase
boundary when the magnetic transition is mainly driven by a proliferation of
vacancies. Adiabatic heating occurs in moving away from the phase boundary. The
isentropes of the half-filled FHM have a relatively simple structure, running
parallel to the temperature axis in the paramagnetic phase, and then curving
upwards as the antiferromagnetic transition occurs. However, in the doped case,
where two magnetic phase boundaries are crossed, the isentrope topology is
considerably more complex
On the number of representations providing noiseless subsystems
This paper studies the combinatoric structure of the set of all
representations, up to equivalence, of a finite-dimensional semisimple Lie
algebra. This has intrinsic interest as a previously unsolved problem in
representation theory, and also has applications to the understanding of
quantum decoherence. We prove that for Hilbert spaces of sufficiently high
dimension, decoherence-free subspaces exist for almost all representations of
the error algebra. For decoherence-free subsystems, we plot the function
which is the fraction of all -dimensional quantum systems which
preserve bits of information through DF subsystems, and note that this
function fits an inverse beta distribution. The mathematical tools which arise
include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review
Identical Particles and Permutation Group
Second quantization is revisited and creation and annihilation operators
areshown to be related, on the same footing both to the algebra h(1), and to
the superalgebra osp(1|2) that are shown to be both compatible with Bose and
Fermi statistics.
The two algebras are completely equivalent in the one-mode sector but,
because of grading of osp(1|2), differ in the many-particle case.
The same scheme is straightforwardly extended to the quantum case h_q(1) and
osp_q(1|2).Comment: 8 pages, standard TEX, DFF 205/5/94 Firenz
Q-derivatives, coherent states and squeezing
We show that the q-deformation of the Weyl-Heisenberg (q-WH) algebra naturally arises in discretized systems, coherent states, squeezed states and systems with periodic potential on the lattice. We incorporate the q-WH algebra into the theory of (entire) analytical functions, with applications to theta and Bloch functions
Topological origin of the phase transition in a mean-field model
We argue that the phase transition in the mean-field XY model is related to a
particular change in the topology of its configuration space. The nature of
this topological transition can be discussed on the basis of elementary Morse
theory using the potential energy per particle V as a Morse function. The value
of V where such a topological transition occurs equals the thermodynamic value
of V at the phase transition and the number of (Morse) critical points grows
very fast with the number of particles N. Furthermore, as in statistical
mechanics, also in topology the way the thermodynamic limit is taken is
crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the
text. To appear in Physical Review Letter
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